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AMS 518, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization
The course provides a thorough treatment of advance risk measurement and portfolio optimization, extending the traditional approaches to these topics by combining distributional models with risk of performance measures into one framework. It focuses on, among others, the fundamentals of probability metrics and optimization, new approahes to portfolio optimization and a vaierty of essential risk measures. Numerical exercises and projects in a high-level programming environment will be assigned.

Offered FALL semester, Prerequisite:  AMS 512 or Instructor Consent
3 credits, ABCF grading 


Course Materials  (recommended):

"Introduction to Risk Parity and Budgeting (Chapman and Hall/CRC Financial Mathematics Series)" by Thierry Roncalli; 1st edition; 2014; Springer Finance; ISBN: 978-1482207156

"Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures" by Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi; Wiley 2008; ISBN:  9780470253601

"Financial Modelling with Jump Processes" by Rama Cont, Peter Tankov; 2nd edition; Taylor & Francis 2015; ISBN: 9781420082197 (NOT available until December 2018)

"Financial Models with Levy Processes and Volatility Clustering" by Svetlozar T. Rachev, Young Shin Kim, Michele L. Bianchi and Frank J. Fabozzi, ISBN: 978-0-470-48235-3


Learning Outcomes:

1) Understand the concepts of probability and optimization
      * Continuous probability distributions and probabilistic inequalities;
      * Unconstrained/constrained optimization.

2) Understand the definitions of risk and uncertainty
      * Value-at-risk;
      * Average VaR;
      * Backtesting risk measures.

3) Demonstrate skills in building portfolio allocation
      * Mean-variance optimization problems, and mean-risk problems;
      * Reward-to-Risk ratios.

4) Understand the method of adaptive data cleaning and basic stylized facts.

5) Understand the model of seasonal volatility and realized volatility dynamics.

6) Demonstrate skill with forecasting risk and return and correlation/multivariate risk.

7) Understand the trading models and theory of heterogeneous markets.

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